Some criteria for solvability and supersolvability

Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University (PNU), Tehran, Iran

Abstract

Denote by $ G $ a finite group, by  $ {\rm hsn}(G) $ the harmonic mean Sylow number (eliminating the Sylow numbers that are one) in $G$ and by    $ {\rm gsn}(G) $ the geometric mean Sylow number (eliminating the Sylow numbers that are one) in $G$. In this paper, we prove that if either $ {\rm hsn}(G)<45/7 $ or  $ {\rm gsn}(G)< \sqrt[3]{300} $, then $G$ is solvable. Also, we show that if either $ {\rm hsn}(G)<24/7 $ or  $ {\rm gsn}(G)<\sqrt{12} $, then $G$ is supersolvable.

Keywords

References

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History

  • Receive Date: 07 August 2022
  • Revise Date: 27 December 2022
  • Accept Date: 28 January 2023

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